Formulate and solve an appropriate integer programming model:
In preparing for a two-week camping vacation, a family must decide how many of each of six items should be loaded into their sport-utility vehicle. The weight and perceived benefit (Where a larger benefit value indicates a more useful item) of each of the items are given in the attached file. The family's vehicle can safely carry no more than 120 pounds of these items, given the amount of luggage that has already been loaded into the vehicle. In trying to decide what should be taken on the vacation, the family must ensure that at least half of the total weight of all objects taken is derived from the inclusion of items of type 1, 2, and 3. Also, the family must ensure that at most half of the total benefit of all objects taken is derived from the inclusion of items of type 4, 5, and 6.
Objective:
Formulate and solve an appropriate integer programming model to help this family decide how many units of each type of item to take to maximize the total benefit to be achieved.
SUVLoading:
Data on items:
Item 1 Item 2 Item 3 Item 4 Item 5 Item 6
Benefit 10 15 17 19 28 22
Weight 3 4 5 6 7 6
Number of each item to be included:
Item 1 Item 2 Item 3 Item 4 Item 5 Item 6
Weight constraint:
Actual Maximum
120
Constraint on Items 1, 2, & 3
Item 1 Weight Item 2 Weight Item 3 Weight Actual sum of weights Minimum required
Constraint on Items 4, 5 & 6
Item 4 Benefit Item 5 Benefit Item 6 Benefit Actual sum of benefits Maximum allowed
Total benefit: